Maybe the answer lies in the music of Bobby Fuller, self-styled “Rock’n’Roll King of the Southwest”, who died on 18 July 1966, aged 23, in mysterious circumstances. Throughout the early 60s – working variously as a songwriter, performer, producer, label-owner and impresario – Fuller carved out a unique sound, blending southern styles and drawing heavily on the stripped-down, raw, heart-on-sleeve rock’n’roll of Buddy Holly, Ritchie Valens and Eddie Cochran. To those elements he added vocal harmonies styled on the Everly Brothers and searing blasts of surf guitar and garage rock fuzz bass. It was a purely American music – one that didn’t acknowledge the Beatles or other British bands then making an impact in America.

“Contrary to popular belief, American music was alive and well before the British Invasion,” says Miriam Linna. Her book I Fought the Law: the Life and Strange Death of Bobby Fuller, titled after its subject’s biggest hit, makes a compelling case for a re-evaluation of Fuller as a pivotal figure in American pop music. “My brother was ahead of his time,” says Randy Fuller, Bobby’s younger sibling and bass player for the Bobby Fuller Four, who co-wrote the book with Linna.

Randy recalls that his brother liked to say the Beatles would “never be able to do Buddy Holly like Buddy Holly because they’re not from Texas”. In other words, they didn’t have the cadence or the swing; unable to tap into a rich vein of regional music that included southern blues and R&B, western swing and Tejano, from south of the border, they couldn’t rock’n’roll like boys from the south. That propulsive rhythm is what drives I Fought the Law, a top 10 hit in March 1966 for the Bobby Fuller Four, who gamely performed it on TV shows such as Hullabaloo and Shivaree, in jailhouse sets or backed by hot-stepping cowgirl go-go dancers brandishing six-shooters. With their distinctive Jay Sebring haircuts, Beatle boots and tailored suits, the Bobby Fuller Four looked curiously out-of-step with their shaggier and more outre peers on the Los Angeles music scene.

I Fought the Law has become the archetypal outlaw rock’n’roll anthem, and has been covered more than 50 times, by the likes of Bruce Springsteen, Tom Petty and, most famously, the Clash. Although the song was written by Buddy Holly’s friend Sonny Curtis and originally performed by the Crickets in 1960, it was Fuller’s version, with its intense, frenetic energy, that popularised the song and drew generations of punks and rockers to it. The song’s success served to overshadow Fuller’s own formidable talents as a writer and arranger of pounding, anthemic odes to teenage heartbreak, such as Let Her Dance and Never to Be Forgotten. Bob Dylan was apparently so enamoured with Fuller’s slow-burning ballad A New Shade of Blue that he applied new lyrics to the melody to make Soon After Midnight on his 2012 album, Tempest – claiming the songwriting credits for himself.

Fuller was a hometown hero in El Paso long before he hit the national charts. In 1961, aged 19, he built his own studio in the den of his parents’ three-bedroom, two-bathroom home there, recording initially on a Viking reel-to-reel tape deck, before gradually acquiring more and better equipment. “If it was the tape recorder that Bob Keane used to do La Bamba with, he got it,” Randy says. “And he would talk my mom and dad into buying it for him.” The brothers built their own control booth and echo chamber, and Fuller started two labels, Eastwood and Exeter, to release his music. In 1964, inspired by what he saw and heard at surf music pioneer Dick Dale’s Rendezvous Ballroom on a trip to California, Fuller opened his own teen club in El Paso (also called the Rendezvous). His group, then known as the Fanatics, were the house band. “It was a sight to behold,” says Randy, “playing surf music in El Paso at our teen club.”

Teenage desert rats flocked to the club dressed as surfers and beach bums. Bobby became a local sensation. “England has the Beatles but El Paso has Bobby,” the El Paso Herald Post crowed in September 1964. The group experienced Beatles-style teen adulation on a local level. An appearance at a local shopping center drew “6,000 screaming and cheering boys and girls”, the paper noted. “It was like something was about to happen and you knew it,” Randy says.

By the close of 1964, they had outgrown El Paso and upped sticks to California, where they looked up Bob Keane, owner of Del-Fi Records, who had discovered and produced Valens and had expressed a prior interest in the band. Keane duly signed them, becoming their manager, booker, producer, label boss and publisher. Years of playing across the southwest had honed the newly christened Bobby Fuller Four into a formidable live group who wowed the Hollywood music scene. The top 10 success of I Fought the Law in the spring of 1966 turned them into teen idols almost overnight.

Things quickly soured, though. Keane’s attempts to mould Fuller into a Valens-style star alienated the rest of the band, and Fuller himself became dissatisfied with the direction in which Keane was pushing the group and with a punishing tour schedule that kept them out of the studio. Although known to eschew gimmicks and overdubs in favour of producing recordings that could be recreated on stage, it was gimmicks that would ultimately stifle Fuller’s career. Keane came up with a succession of dumb marketing ideas for the group: a single released as the Shindigs to secure a slot on the music TV show Shindig!; a drag racing-themed debut long-player, branded with the name of the Los Angeles radio station KRLA; a cameo in The Ghost in the Invisible Bikini – a goofy beach party movie starring Boris Karloff – lip-synching to songs behind Nancy Sinatra. And, it may have been gimmicks that killed Bobby Fuller, too.

On the afternoon of 18 July 1966, Fuller was found dead by his mother in her blue Oldsmobile. Initial reports pointed to suicide: “Musician Robert Fuller, 23, was found dead on the parking lot at his Hollywood apartment house with a plastic hose in his hands leading to a gasoline can,” the LA Times reported. That’s how the police saw it, too, closing the case without even brushing for fingerprints or interviewing anyone. The details told a different story. The car had not been in the lot 30 minutes before his mother found it, yet Fuller’s body was in an advanced state of rigor mortis, suggesting he had died elsewhere.

Various theories have been advanced about Fuller’s death, most wildly implausible: an accident following a bad reaction to LSD; knocked off by the Manson family; retribution for a dalliance with the girlfriend of a mob-connected Los Angeles nightclub owner. One theory even implicated Keane, noting that Fuller was the third artist under his charge, after Valens and Sam Cooke, to die in disputed circumstances.

While Linna’s book doesn’t solve the mystery, it does offer up the name of somebody whose entry into Fuller’s life was a bad omen: Morris Levy, owner of Roulette Records, a notorious figure once described as the “Godfather of the American music business”. Levy’s business partners and associates read like a roll call of the east-coast mafia, and included members of the Gambino, Genovese and DeCavalcante crime families. The book catalogues the grim history of beatings, threats and deaths of those associated with Levy.

Shortly before Fuller’s death, Keane’s label had signed an exclusive distribution deal with Roulette, and the Bobby Fuller Four’s last single, The Magic Touch, a Motown-style soul number picked by Keane to piggyback another musical fad, was penned by a songwriter associated with Roulette. Randy believes it is likely that his brother’s death was connected to a business deal he wanted to back out of. He recalled seeing his brother and Keane in the company of a third man during the Bobby Fuller Four’s spring 1966 stay in New York, although he could not remember who it was. When shown a photo of Levy by Linna, Randy identified him without knowing his name.

Randy believes that, had he lived, Bobby might have returned to El Paso, opened a new teen club and continued his experiments in the studio, free from interference and commercial pressures. If so, he would almost certainly be thought of now as a seminal and visionary figure, along the lines of Brian Wilson, Phil Spector or Joe Meek. Linna, too, is convinced Fuller was destined for more than cult success, pointing to the fact that a UK tour had been booked for the Bobby Fuller Four. “If that had happened, I honestly believe today’s music scene would be vastly different,” she says. “[Fuller] would have represented the second coming of Buddy Holly, who eight years earlier had toured Britain, inspiring everyone from the fledgling Beatles to those guys who ended up being in a band called the Rolling Stones.”

And maybe, just maybe, the Bobby Fuller Four would have spearheaded an American Invasion of Britain.

•I Fought The Law: The Life and Strange Death of Bobby Fuller is available from Kicks Books.